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MATH 3A CHAPTER 12 POWERPOINT PRESENTATION

MATH 3A CHAPTER 12 POWERPOINT PRESENTATION. GEOMETRY AND IMAGINATION. LEARNING TARGETS. AFTER YOU COMPLETE THIS CHAPTER, YOU WILL BE ABLE TO: IDENTIFY HOW GEOMETRIC FIGURES INTERSECT IN SPACE. WRITE EQUATIONS FOR LOCI. CONNECT SIMPLE AND COMPOUND LOCI. DESCRIBE COMPOUND LOCI.

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MATH 3A CHAPTER 12 POWERPOINT PRESENTATION

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  1. MATH 3A CHAPTER 12 POWERPOINT PRESENTATION GEOMETRY AND IMAGINATION

  2. LEARNING TARGETS • AFTER YOU COMPLETE THIS CHAPTER, YOU WILL BE ABLE TO: • IDENTIFY HOW GEOMETRIC FIGURES INTERSECT IN SPACE. • WRITE EQUATIONS FOR LOCI. • CONNECT SIMPLE AND COMPOUND LOCI. • DESCRIBE COMPOUND LOCI.

  3. LINES IN THE PLANE AND IN SPACE • IN THE PLANE: FOR A 2-D FIGURE, IT IS EASY TO THINK ABOUT LINES LIKE A RADIUS OR A DIAMETER. THE LOCUS OF POINT FROM A GIVEN CENTER IS A CIRCLE. • IN SPACE: THE LOCUS OF POINTS IN SPACE AT EQUAL DISTANCES FROM A GIVEN POINT IS A SPHERE.

  4. EXAMPLES:LINES IN THE PLANE

  5. LINES IN SPACE

  6. PLANES THAT INTERESECT

  7. PARTS OF A SPHERE

  8. CYLINDERS (Intersected by a plane)

  9. More Pictures

  10. Loci In The Coordinate Plane • Think of parallel lines, horizontal lines, vertical lines. When they are on a graph, the locations of the points can be used to solve many problems. • Finding a midpoint, the equidistant locus, perpendicular bisectors, locus of points that forma circle. All of this is how we discover the loci in the coordinate plane.

  11. Examples – Perpendicular Bisector and Midpoint

  12. Loci for a Circle

  13. Equation for a Circle

  14. Equation for a Circle • r² = x² + y²

  15. COMPOUND LOCI • YOU HAVE LEARNED HOT TO VISUALIZE LOCI, NOW WE WILL LOOK AT LOCI THAT SATISFY MORE THAN ONE CONDITION AT A TIME CALLED COMPOUND LOCI.

  16. LOCI IN VARIOUS SHAPES

  17. Loci in Space

  18. Now – Use Your Imagination to Figure Out How Shapes Intersect in the Real World

  19. More

  20. Can You Find Some Other Examples • In machines • In buildings • In bridges • In cars, trucks, planes, ships, busses • In chemistry, medicine • In nature?????

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